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Research Papers

Exact Solutions for the Generalized Euler’s Problem

[+] Author and Article Information
Q. S. Li

Department of Building and Construction, City University of Hong Kong, Kowloon, Hong Kong, P.R.C.

J. Appl. Mech 76(4), 041015 (Apr 27, 2009) (9 pages) doi:10.1115/1.2937151 History: Received September 15, 2007; Revised March 18, 2008; Published April 27, 2009

This paper is concerned with buckling analysis of a nonuniform column with classical∕nonclassical boundary conditions and subjected to a concentrated axial force and distributed variable axial loading, namely, the generalized Euler’s problem. Exact solutions are derived for the buckling problem of nonuniform columns with variable flexural stiffness and under distributed variable axial loading expressed in terms of polynomial functions. Then, more complicated buckling problems are considered such as that the distribution of flexural stiffness of a nonuniform column is an arbitrary function, and the distribution of axial loading acting on the column is expressed as a functional relation with the distribution of flexural stiffness and vice versa. The governing equation for such problems is reduced to Bessel equations and other solvable equations for seven cases by means of functional transformations. A class of exact solutions for the generalized Euler’s problem involved a nonuniform column subjected to an axial concentrated force and axially distributed variable loading is obtained herein for the first time in literature.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

A H-H column subjected to a concentrated axial force at its top and a distributed axial force

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Figure 2

The buckling mode of a H-H column

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Figure 3

A C-F column subjected to a concentrated axial force at its top and a distributed axial force

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Figure 4

The buckling mode of a C-F column

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Figure 5

Comparison among the three special cases

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Figure 6

Sketch of a high-rise structure

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